Write as a Vector Equality

Problem

{[x2−4*x3+3*x4=2],[x−5*x2−6*x3+3*x4=3],[−3*x4=15],[5*x3−4*x4=10])

Solution

1. Identify the variables present in the system of equations, which are x x2 x3 and x4

2. Rewrite each equation so that the coefficients of x x2 x3 and x4 are clearly aligned, including zero coefficients where a variable is missing.

3. Express the system as a linear combination of vectors, where each vector contains the coefficients of one specific variable across all equations.

4. Set the sum of these scaled vectors equal to the vector of constants from the right-hand side of the equations.

Final Answer

x*[[0],[1],[0],[0]]+x2*[[1],[−5],[0],[0]]+x3*[[−4],[−6],[0],[5]]+x4*[[3],[3],[−3],[−4]]=[[2],[3],[15],[10]]

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